Equal profit and loss distances from cost: Selling a pair of shoes for ₹ 2,033 yields a profit equal in magnitude to the loss incurred when selling it for ₹ 1,063. What is the cost price of the shoes?

Introduction / Context:
When equal absolute profit and loss occur at two selling prices, the cost price lies exactly midway between those two prices because the deviations above and below cost are equal.

Given Data / Assumptions:

• SP_high = ₹ 2,033 gives a profit of amount x.
• SP_low = ₹ 1,063 gives a loss of the same amount x.

Concept / Approach:
Let CP be the midpoint: CP = (SP_high + SP_low)/2.

Step-by-Step Solution:
CP = (2,033 + 1,063) / 2 = 3,096 / 2 = ₹ 1,548

Verification / Alternative check:
Profit at 2,033: 2,033 − 1,548 = ₹ 485. Loss at 1,063: 1,548 − 1,063 = ₹ 485, equal magnitudes as required.

Why Other Options Are Wrong:

• ₹ 1,650 / ₹ 1,532: not the arithmetic mean; they break symmetry.
• Cannot be determined: symmetry fully determines CP.

Common Pitfalls:

• Using percentage equality instead of rupee equality (the statement is about equal amounts, not equal percentages).

Final Answer:
₹ 1548